Scale-dependent permeability and formation factor in porous media: Applications of percolation theory

Esmaeilpour, Misagh; Ghanbarian, Behzad; Liang, Feng; Liu, Hui‐Hai

doi:10.1016/j.fuel.2021.121090

Cited by 23 publications

(14 citation statements)

References 68 publications

(119 reference statements)

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“…The increasing trend in the scale dependence of the permeability was reported by Esmaeilpour et al. (2021) who simulated flow in Networks 1 to 3 with Z = 6 (see their Figures 5–7). They did not, however, utilize finite‐size scaling analysis to explain the scale dependence of the permeability in such networks.…”

Section: Resultssupporting

confidence: 72%

Effect of Pore‐Scale Heterogeneity on Scale‐Dependent Permeability: Pore‐Network Simulation and Finite‐Size Scaling Analysis

Ghanbarian

Esmaeilpour

Ziff

et al. 2021

Water Resources Research

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Flow and transport in porous media are typically investigated at four main length scales, namely, pore, core, lysimeter, and field scales. Accordingly, a long-standing problem in subsurface hydrology has been relating a property's value at one scale, for example, field, to its value at another scale, such as the core scale. This process, called scaling, has been a subject of active research in the past several decades (see, e.g.,

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Section: Resultssupporting

confidence: 72%

Effect of Pore‐Scale Heterogeneity on Scale‐Dependent Permeability: Pore‐Network Simulation and Finite‐Size Scaling Analysis

Ghanbarian

Esmaeilpour

Ziff

et al. 2021

Water Resources Research

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“…Laboratory data further support the idea that permeability increases with spatial scale (e.g., Schulze‐Makuch et al., 1999). However, simulations indicate that permeability can both increase and decrease with spatial scale (e.g., Esmaeilpour et al., 2021; Ghanbarian, 2022; Nordahl & Ringrose, 2008; Sahimi et al., 1986). Consequently, this previous work demonstrates that varying the spatial scale in three‐dimensions can change estimates of permeability, and the present analysis demonstrates that it is similarly difficult to estimate the three‐dimensional tortuosity (and thus permeability) from two‐dimensional observations.…”

Section: Discussionmentioning

confidence: 99%

Deriving Three‐Dimensional Properties of Fracture Networks From Two‐Dimensional Observations in Rocks Approaching Failure Under Triaxial Compression: Implications for Fluid Flow

McBeck

Renard

2022

Water Resources Research

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“…The retention curve gives the matrix potential (or capillary pressure) as a function of saturation under equilibrium conditions 9 , 10 . It was shown that the retention curve and other physical properties depend on the volume of the sample 11 – 15 . However, this important issue has not usually been considered in porous media flow modelling.…”

Section: Introductionmentioning

confidence: 99%

The difference between semi-continuum model and Richards’ equation for unsaturated porous media flow

Vodák

Fürst

Šír

et al. 2022

Sci Rep

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Semi-continuum modelling of unsaturated porous media flow is based on representing the porous medium as a grid of non-infinitesimal blocks that retain the character of a porous medium. This approach is similar to the hybrid/multiscale modelling. Semi-continuum model is able to physically correctly describe diffusion-like flow, finger-like flow, and the transition between them. This article presents the limit of the semi-continuum model as the block size goes to zero. In the limiting process, the retention curve of each block scales with the block size and in the limit becomes a hysteresis operator of the Prandtl-type used in elasto-plasticity models. Mathematical analysis showed that the limit of the semi-continuum model is a hyperbolic-parabolic partial differential equation with a hysteresis operator of Prandl’s type. This limit differs from the standard Richards’ equation, which is a parabolic equation and is not able to describe finger-like flow.

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Scale-dependent permeability and formation factor in porous media: Applications of percolation theory

Cited by 23 publications

References 68 publications

Effect of Pore‐Scale Heterogeneity on Scale‐Dependent Permeability: Pore‐Network Simulation and Finite‐Size Scaling Analysis

Effect of Pore‐Scale Heterogeneity on Scale‐Dependent Permeability: Pore‐Network Simulation and Finite‐Size Scaling Analysis

Deriving Three‐Dimensional Properties of Fracture Networks From Two‐Dimensional Observations in Rocks Approaching Failure Under Triaxial Compression: Implications for Fluid Flow

The difference between semi-continuum model and Richards’ equation for unsaturated porous media flow

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